Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters

Shanshan Lv; Mingshun Jiang; Chenhui Su; Lei Zhang; Faye Zhang; Qingmei Sui; Lei Jia

doi:10.1364/AO.58.0000A7

Applied Optics
Vol. 58,
Issue 5,
pp. A7-A12
(2019)
•https://doi.org/10.1364/AO.58.0000A7

Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters

Shanshan Lv, Mingshun Jiang, Chenhui Su, Lei Zhang, Faye Zhang, Qingmei Sui, and Lei Jia

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Shanshan Lv, Mingshun Jiang, Chenhui Su, Lei Zhang, Faye Zhang, Qingmei Sui, and Lei Jia, "Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters," Appl. Opt. 58, A7-A12 (2019)

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Abstract

Fringe projection profilometry (FPP) technology is an important method for 3D reconstruction. In this paper, we proposed a flexible calibration method of an FPP system based on the imaging principle and geometrical structure of the system. The target coordinates are only related to its pixel coordinates and phase. First, the fringe images are projected onto the calibration plate, and the phase can be calculated through the four-step phase-shifting method. Then, the pixel coordinates of the feature points can be located with the binarized fringe images and the centroid method. Finally, the calibration parameters are calculated by the nonlinear least-squares method (NLSM). The reconstructed experiment of 162 testing points was carried out, and the result shows that the maximum relative errors on coordinates $X$ , $Y$ , and $h$ are 0.27%, 0.42%, and 0.59%, respectively. The other two surface reconstruction experiments also verify the feasibility of the calibration method.

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Corrections

Shanshan Lv, Mingshun Jiang, Chenhui Su, Lei Zhang, Faye Zhang, Qingmei Sui, and Lei Jia, "Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters: publisher’s note," Appl. Opt. 58, 1298-1298 (2019)
https://opg.optica.org/ao/abstract.cfm?uri=ao-58-5-1298

24 January 2019: A correction was made to the Funding section.

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$h$		$X$		$Y$
$a_{1}$	695.5456	$b_{1}$	$1.85 e - 7$	$c_{1}$	$6.34 e - 8$
$a_{2}$	0.0416	$b_{2}$	0.0154	$c_{2}$	0.0085
$a_{3}$	0.9106	$b_{3}$	0.0085	$c_{3}$	0.0084
$a_{4}$	−87.1476	$b_{4}$	−2.7499	$c_{4}$	3.1827
Resnorm	$1.66 \times 10^{- 11}$	Resnorm	$3.82 \times 10^{- 5}$	Resnorm	$1.64 \times 10^{- 4}$

Testing	T1 (30 mm)			T2 (40 mm)
Testing	$X$	$Y$	$h$	$X$	$Y$	$h$
MAX	0.27%	0.42%	0.59%	0.23%	0.40%	0.38%
RMS	$1.74 \times 10^{- 6}$	$1.56 \times 10^{- 6}$	$9.16 \times 10^{- 8}$	$1.41 \times 10^{- 6}$	$1.47 \times 10^{- 6}$	$6.76 \times 10^{- 7}$

Testing Object	The Ladder			The Cube
Testing Object	$L$	$W$	$H_{1}$	$H_{2}$
Theoretical value (mm)	35.47	50.57	62.58	111.01
Measured value (mm)	35.20	51.072	62.87	110.797
Relative error	0.76%	0.99%	0.46%	0.19%

$h$		$X$		$Y$
$a_{1}$	695.5456	$b_{1}$	$1.85 e - 7$	$c_{1}$	$6.34 e - 8$
$a_{2}$	0.0416	$b_{2}$	0.0154	$c_{2}$	0.0085
$a_{3}$	0.9106	$b_{3}$	0.0085	$c_{3}$	0.0084
$a_{4}$	−87.1476	$b_{4}$	−2.7499	$c_{4}$	3.1827
Resnorm	$1.66 \times 10^{- 11}$	Resnorm	$3.82 \times 10^{- 5}$	Resnorm	$1.64 \times 10^{- 4}$

Testing	T1 (30 mm)			T2 (40 mm)
Testing	$X$	$Y$	$h$	$X$	$Y$	$h$
MAX	0.27%	0.42%	0.59%	0.23%	0.40%	0.38%
RMS	$1.74 \times 10^{- 6}$	$1.56 \times 10^{- 6}$	$9.16 \times 10^{- 8}$	$1.41 \times 10^{- 6}$	$1.47 \times 10^{- 6}$	$6.76 \times 10^{- 7}$

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Applied Optics